Stir together yeast, honey, and 1/2 cup warm water in a large bowl, then let stand until foamy, about 5 minutes.,(If mixture doesn't foam, discard and start over with new yeast.),While yeast mixture stands, stir together flours in another bowl.,Whisk 1/2 cup flour mixture into yeast mixture until smooth, then cover with plastic wrap and let stand in a draft-free place at warm room temperature until doubled in bulk and bubbly, about 45 minutes.,Stir in oil, salt, remaining 3/4 cup warm water, and remaining 2 1/2 cups flour mixture until a dough forms.,Turn out dough onto a floured surface and knead, working in just enough additional flour to keep dough from sticking, until dough is smooth and elastic, 8 to 10 minutes.,Form dough into a ball and put in an oiled large bowl, turning to coat.,Cover bowl with plastic wrap and let dough rise in draft-free place at warm room temperature until doubled in bulk, about 1 hour.,______,Form each piece into a ball.,Flatten 1 ball, then roll out into a 6 1/2- to 7-inch round on floured surface with a floured rolling pin.,Transfer round to 1 of 2 baking sheets lightly sprinkled with cornmeal.,Make 7 more rounds in same manner, arranging them on baking sheets.,Loosely cover pitas with 2 clean kitchen towels (not terry cloth) and let stand at room temperature 30 minutes.,Set oven rack in lower third of oven and remove other racks.,Preheat oven to 500F.,Transfer 4 pitas, 1 at a time, directly onto oven rack.,Bake until just puffed and pale golden, about 2 minutes.,Turn over with tongs and bake 1 minute more.,Cool pitas on a cooling rack 2 minutes, then stack and wrap loosely in a kitchen towel to keep pitas warm.,Bake remaining 4 pitas in same manner.,Serve warm.